What is the word for the verb that signifies performing the action suggested by a given noun?

While I am unaware of any specific word for this, I would call the blank in each example sentence (or the first blank in the last example sentence) a verbal antecedent.

This is a mix of the two normal senses of the word antecedent (along with the definition of verbal in its sense of grammar rather than speech):

[Merriam-Webster]

1 grammar : a substantive word, phrase, or clause whose denotation is referred to by a pronoun (such as John in "Mary saw John and called to him")

broadly : a word or phrase replaced by a substitute

2 a : a preceding event, condition, or cause
// events that were antecedents of the war

2 b antecedents plural : the significant events, conditions, and traits of one's earlier life

Neither sense directly matches, but the combination of the two does.

In other words, the examples could be rephrased::

The verbal antecedent of "mistake" is "make."
→ She [made] something. She [made] a mistake.

The verbal antecedent of "action" is "perform."
→ He [performed] something. He [performed] an action.

The verbal antecedent of "campaign" is "planned."
→ They [planned] something. They [planned] a campaign.

In the first example, for instance, make is the verb that antecedes the noun mistake.

And in the last example, other verbs could also be used, such as conducted or launched, as suggested in a comment under the question, or executed.

Which verbs commonly go with which nouns could be called collocations.